Visualization is a descriptive way to ensure the audience attention and to make people better understand the content of a given topic. Nowadays, in the world of science and technology, visualization has become a necessity. However, it is a huge challenge to visualize varying amounts of data in a static or dynamic form. In this paper we describe the role, value and importance of visualization in maths and science. In particular, we are going to explain in details the benefits and shortages of visualization in three main domains: Mathematics, Programming and Big Data. Moreover, we will show the future challenges of visualization and our perspective how to better approach and face with the recent problems through technical solutions.

Here we discuss the path integral formalism for quantization of fields. The basic idea is reviewed and explained. This is completely based on the book ``Quantum Field Theory A Modern Introduction" by Michio Kaku. For calculation natural system of units is taken.

In mathematics, a rational number is any number that can be expressed as the quotient
or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q
may be equal to 1, every integer is a rational number. The set of all rational numbers,
often referred to as ”the rationals”, is usually denoted by a boldface Q (or blackboard
bold , Unicode ); it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian
for ”quotient”. The decimal expansion of a rational number always either terminates
after a finite number of digits or begins to repeat the same finite sequence of digits over
and over. Moreover, any repeating or terminating decimal represents a rational number.
These statements hold true not just for base 10, but also for any other integer base (e.g.
binary, hexadecimal). A real number that is not rational is called irrational. Irrational
numbers include √2, , e, and . The decimal expansion of an irrational number continues
without repeating. Since the set of rational numbers is countable, and the set of real
numbers is uncountable, almost allreal numbers are irrational.

As of this writing, the algorithm employed for difficulty adjustment in the CryptoNote reference code is known by the Monero Research Lab to be flawed. We describe and illustrate the nature of the flaw and recommend a solution. By dishonestly reporting timestamps, attackers can gain disproportionate control over network difficulty. We verify this route of attack by auditing the CryptoNote reference difficulty adjustment code, which, we reimplement in the Python programming language. We use a stochastic model of blockchain growth to test the CryptoNote reference difficulty formula against the more traditional Bitcoin difficulty formula. This allows us to test our difficulty formula against various hash rate scenarios. This research bulletin has not undergone peer review, and reflects only the results of internal investigation.